1. Warm Up – August 23, 2017 How is each function related to y = x?
y = x – 3 2. y = 2x 3. y = -4x
Write an equation for each vertical translation of y = x.
4. 2/3 unit down units up
Write the function rule for the function related in the given axis.
6. f(x) = 3x; y-axis
Write the function rule g(x) after the given transformation of the graph f(x) = 4x.
7. Translated up 5 units; reflection in the y-axis
8. Reflection in the y-axis; vertical compression by a factor of 1/8.

2. 2.7 Absolute‐Value Functions and Graphs
Learning Target: I can graph absolute‐value functions. Key Terms: absolute‐value functions, axis of symmetry, vertex

3. Absolute‐value functions – function of the form f(x) = |mx + b| + c, where m ≠ 0, is an absolute value function. Axis of symmetry – the line that divides a figure into two parts that are mirror images. Vertex – single maximum or minimum of a graph

4. Absolute-Value Parent Function
f(x) = |x|

5. “I do” Graphing an Absolute‐Value Function
What is the graph of the absolute value function y = |x| ‐ 4? How is this graph different from the graph of the parent function y = |x|?

6. “You do”
What is the graph of the function y = |x| + 2? How is this graph different from the parent function? Do transformations of the form y = |x| + k affect the axis of symmetry? Explain.

7. The Family of Absolute Value Functions
Parent Function y = |x|
Vertical Translation
Horizontal Translation
Translation up k units, k > 0
y = |x| + k
Translation down k units, k > 0
y = |x| - k
Translation up h units, h > 0
y = |x – h|
Translation down h units, h > 0
y = |x + h|
Vertical Stretch and Compression
Vertical stretch, a > 1
y = a|x|
Vertical compression, 0 < a < 1
Reflection
In the x-axis
y = -|x|
In the y-axis
y = |-x|

8. “I do” Combining Translations
What is the graph of y = |x + 2| + 3?

9. “You do”
What is the graph of y = |x – 2| + 1?

10. “I do” Vertical Stretch and Compression
What is the graph of y = ½|x|?

11. “You do”
What is the graph of y = 2|x|?

12. General Form of the Absolute Value Function
y = a|x – h| + k The stretch or compression factor is |a|, the vertex is located at (h, k), and the axis of symmetry is the line x – h

13. “I do” Identifying Transformations
Without graphing, what are the vertex and axis of symmetry of the graph of y = 3|x – 2| + 4? How is the parent function y = |x| transformed?

14. “You do”
What are the vertex and axis of symmetry of y = ‐2|x – 1| ‐ 3? How is y = |x| transformed?

15. Homework
Pg. 111 # 10, 12, 16, 17, 18, 23, 24, 32